SSC JE Civil Engineering 23-Mar-2021 Shift 1 Paper

Concept:
U tube differential manometer:● A U tube differential manometer is a type of differential manometer which is used to measure the difference of pressure between the two points of the pipes.
● U tube manometer's connected pipes may be at the same level and the different level lets see both one by one.
(a) When the pipes are at the same levelIn this type of u tube differential manometer, both ends of the pipes will be at the same level, and by using the hydrostatic law and the balancing the column method we may calculate the pressure difference between the points P & Q in a pipe.
${\mathrm{P}}_{\mathrm{p}}-{\mathrm{P}}_{\mathrm{q}}=\mathrm{g}\mathrm{h}\left(\mathrm{\rho }-{\mathrm{\rho }}_1\right)$
Where ${\mathrm{P}}_{\mathrm{p}}=$ Pressure at point $\mathrm{P},{\mathrm{P}}_{\mathrm{q}}=$ Pressure at point $\mathrm{Q},\mathrm{\rho }=$ Density of fluid
(b)When the pipes are at the different level
In this type of u tube differential manometer, both ends of the connected pipes are not at the same level, and by using the hydrostatic law and the balancing the column method we may find the pressure difference between the two points (P & Q) of the pipe.${\mathrm{P}}_{\mathrm{p}}-{\mathrm{P}}_{\mathrm{q}}=\mathrm{h}\left(\mathrm{\rho }\mathrm{g}-{\mathrm{h}}_1{\mathrm{\rho }}_1+{\mathrm{h}}_2{\mathrm{\rho }}_2\right)$
Where ${\mathrm{P}}_{\mathrm{p}}=$ Pressure at point $\mathrm{P},{\mathrm{P}}_{\mathrm{q}}=$ Pressure at point $\mathrm{Q},\mathrm{\rho }=$ Density of fluid
Hence, A horizontal pipeline AB of diameter d conveys water, flowing from A to B. The U-tube manometer with mercury as the manometric liquid can be used for the measurement of the difference in the pressure head between two points A and B.